Consider the repeated game in which the following stage game is played twice in succession, with payoffs averaged between the two rounds (and no discounting). d f 0,0 18, 18 48, 10 e а | 4у, 4y 10,0 b 0, 10 0,0 10, 48 40,40

INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. b1 b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of 5 such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)

INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. bị b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of d such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)

1

Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.

Explain all will rate   what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibrium

Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?

In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.

List five types of infinitely repeated games

Player 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.